Solve 2x-1/3+x+4/2<4

$$\frac { 2 x - 1 } { 3 } + \frac { x + 4 } { 2 } < 4$$

Solve for x

$$x<2$$

Solution Steps

Multiply both sides of the equation by 6, the least common multiple of 3,2. Since 6 is positive, the inequality direction remains the same.

$$2\left(2x-1\right)+3\left(x+4\right)<24$$

Use the distributive property to multiply 2 by 2x-1.

$$4x-2+3\left(x+4\right)<24$$

Use the distributive property to multiply 3 by x+4.

$$4x-2+3x+12<24$$

Combine 4x and 3x to get 7x.

$$7x-2+12<24$$

Add -2 and 12 to get 10.

$$7x+10<24$$

Subtract 10 from both sides.

$$7x<24-10$$

Subtract 10 from 24 to get 14.

$$7x<14$$

Divide both sides by 7. Since 7 is positive, the inequality direction remains the same.

$$x<\frac{14}{7}$$

Divide 14 by 7 to get 2.

$$x<2$$